Solve for $n$, $ -\dfrac{4n + 5}{15n + 10} = \dfrac{9}{9n + 6} - \dfrac{6}{12n + 8} $
First we need to find a common denominator for all the expressions. This means finding the least common multiple of $15n + 10$ $9n + 6$ and $12n + 8$ The common denominator is $180n + 120$ To get $180n + 120$ in the denominator of the first term, multiply it by $\frac{12}{12}$ $ -\dfrac{4n + 5}{15n + 10} \times \dfrac{12}{12} = -\dfrac{48n + 60}{180n + 120} $ To get $180n + 120$ in the denominator of the second term, multiply it by $\frac{20}{20}$ $ \dfrac{9}{9n + 6} \times \dfrac{20}{20} = \dfrac{180}{180n + 120} $ To get $180n + 120$ in the denominator of the third term, multiply it by $\frac{15}{15}$ $ -\dfrac{6}{12n + 8} \times \dfrac{15}{15} = -\dfrac{90}{180n + 120} $ This give us: $ -\dfrac{48n + 60}{180n + 120} = \dfrac{180}{180n + 120} - \dfrac{90}{180n + 120} $ If we multiply both sides of the equation by $180n + 120$ , we get: $ -48n - 60 = 180 - 90$ $ -48n - 60 = 90$ $ -48n = 150 $ $ n = -\dfrac{25}{8}$